This site shows upcoming events (mainly concerts) in Japan:
The cheapest way to get the tickets is to directly purchase them on your own from the ticket companies. There are several companies, but unfortunately most of their websites are only in Japanese.
This blog explains how to purchase from well-known site called Ticket PIA:
Here is the place you can get the tickets for baseball and sumo (in English):
The second way is to join a fan club. If you have a specific artist you really like, this might be a choice, but this will require the member to be residing in Japan locally and their notices will be in Japanese.
The third way is to purchase from Auctions (ex. Yahoo Japan Auction). The price will be higher but you can get the ticket without much prior commitment.
The fourth, and the most expensive way is to purchase from reseller stores. This is the easiest since it requires no prior preparation, but the price will of course be higher than the original. There is a famous shop called Gorakudo in Takeshita Street, Harajuku.